In the past, wall structures formed from building blocks, etc. typically have been constructed by the placement of blocks one upon the other, in vertical overlying relationship and in horizontal courses of blocks with mortar in contact with both the horizontal and vertical external surfaces of the blocks. The construction of walls in this manner requires a relatively skilled mason in order to form the wall in an upright attitude and to place the blocks in substantially equally spaced relationship from one another throughout the wall structure. When the wall structure has been formed, it is sometimes found that the wall is out of plumb or that the wall should be changed for some reason. Moreover, the horizontal strength characteristics of conventionally-formed block walls is not particularly good unless the wall is fabricated from relatively thick blocks or unless the wall is formed with additional thicknesses of materials, such as another layer of blocks or bricks. Furthermore, the conventional prior art block walls are not very good heat insulators and moisture usually can easily pass through the wall structure, either through the block material or through the cracks and openings in the mortar between the blocks. The utility of the conventional prior art blocks is limited with respect to tying the blocks together with a hurricane beam or the like, for extending electrical or water conduits horizontally through a wall structure, or for supporting window assemblies in a wall structure. Special modifications of the blocks and of other components of a wall structure must be made to accommodate these and other items that are desired to be present in a typical wall sturcture.